IMABS

Returns the absolute value of a complex number.

Syntax:

IMABS(complexnumber)

complexnumber is text representing a complex number, for example as a+bi or a+bj.

IMABS returns the absolute value or modulus of complexnumber - that is, in a polar representation, the distance from the origin. If complexnumber is a+bi, then the absolute value is $a^{2} + b^{2}$

Example:

IMABS("4+3i")

returns 5.

Application:

Calculating Impedance Magnitude

In AC (Alternating Current) circuits, components like resistors, inductors, and capacitors all contribute to the circuit's impedance, which is a measure of its opposition to current flow. Impedance is a complex number, with a real part representing resistance and an imaginary part representing reactance.

Real Part (Resistance, R): The opposition to current flow that dissipates energy as heat.
Imaginary Part (Reactance, X): The opposition to current flow that stores and releases energy in electric or magnetic fields.

The total impedance, Z, is given by the formula: Z=R+jX, where j is the imaginary unit ( $- 1$ ).

The magnitude of the impedance, |Z|, is a crucial value because it represents the total effective opposition to current flow and is used in Ohm's Law for AC circuits (V=I⋅|Z|). The magnitude of a complex number a+bi is calculated as $a^{2} + b^{2}$ . In a spreadsheet, the IMABS function does this calculation automatically.

Scenario: An electrical engineer is designing a circuit and needs to calculate the total impedance of several components. They have a table of complex impedance values for each component and want to find the magnitude of the total impedance.

	Component	Impedance (Z)
	A	B
1	Resistor-Inductor	15 + 8j
2	Capacitor	5-12j
3	Inductor-Resistor	10+4j
4	Total	30+0j

To find the total impedance, the engineer adds the individual complex impedances: (15+8j)+(5−12j)+(10+4j)=(15+5+10)+(8−12+4)j=30+0j

The magnitude of this total impedance, |Z|, is:

$∣ Z ∣ = 3 0^{2} + 0^{2} = 900 + 0 = 900 = 30$

Using a spreadsheet, this calculation is streamlined with the IMABS function.

Spreadsheet Table Example:

	Component	Impedance (Z)
	A	B
1	Resistor-Inductor	15 + 8j
2	Capacitor	5-12j
3	Inductor-Resistor	10+4j
4	Total Impedance	30+0j
5	Magnitude	30

Explanation:

In cell B5, the IMABS function takes the complex number from cell B4 and calculates its absolute value, or magnitude.

The result in cell B5 would be 30. This magnitude value is then used in further calculations, such as determining the current flowing through the circuit.